Example Project: Bicycle

Example Project: Bicycle#

For the example project I chose to model and examine a bicycle. I chose this because most of us have an intuition of how bicycles should work and move, yet few of us actually understand the underlying dynamics. I therefore set the goal of examining different ways of modelling a bicycle, how different parameters affect the behaviour of the bicycle and lastly what makes a bicycle stable.

Early stage investigation#

The start of any project involves investigating existing literature on your chosen topic. I usually start by looking for relevant Wikipedia pages to find relevant source material. A quick search yielded a comprehensive Wikipedia page for Bicycle and motorcycle dynamics. We’ll note that down, and look in its references. We’ll look for anything that looks relevant to our project. Then we’ll try to look for more colloquial articles which may help us dive gently into the topic. Some quick Google searches later, and we have the following list of potential sources:

These are just some types of sources one might encounter during a literature search. Even though we won’t use them right away, it’s always a good idea to familiarize yourself with literature on your chosen topic. This will give you a good indication of how well researched your system is, and will make it easier to know where to look once you’ve moved passed the initial stage of modelling your system. Luckily for us, bicycles are a well studied topic, so we’ll have no issues comparing our work against others or check that we are on the right track when modelling our system. One important aspect to keep in mind is the even though there exists a lot of different approaches to this topic, we still have to explore them on our own. We can cite sources, compare our work, but it’s not acceptable to copy someone else’s work and then add minor modifications. Keeping this in mind, we’ll move on and take a closer look at the basic elements that make up a bicycle.

import pythreejs as pj
import sympy as sm

from IPython.display import  display
box = pj.BoxGeometry(width=4, height=4, depth=4)
box

Testing different bicycle parameters#

https://imgs.xkcd.com/comics/timeline_of_bicycle_design.png

A good place to start to look for parameters is looking for similar components’ specifications online through different stores or vendors.

Looking at bike wheels etc https://www.sykkelkomponenter.no/sykkeldeler/el-sykkel-deler/hjul/bakhjul-for-skivebrems/m-wave-4-30-e-mtb-12-x-148mm-boost-29-bakhjul

The anatomy of a bicycle#

The first step of modelling any system is to break it down into its most essential components. A bicycle has four basic components:

  1. Bicycle frame: Distributes the loads to all the attached components

  2. Back wheel: Drives the bicycle through a torque from the chain and pedals

  3. Front wheel: Leads the bicycle trajectory

  4. Bicycle fork: Steers the front wheel through a rotating axle

Putting our modelling and simulation glasses on we can now break down each one of these components into different states and parameters. All of these components have mass and inertia, and seen from the perspective of the bicycle frame, the only moving component is the bicycle fork which moves the front wheel. All other components either stay still or rotate in place relative to the bike frame. Before we begin, we’ll have to declare our initial assumptions. It’s crucial that we keep track of assumptions throughout the entire modelling and simulation process. I usually prefer to keep them in a list which we’ll update for every new assumption we make.

Assumptions

  1. All components are rigid bodies: By assuming this we disregard any bending/torsion/elasticity in our components. Effects like vibrations disappear from our model

Starting from this assumption, let’s examine the most essential feature of a bicycle, namely its wheels.

The bike wheel#

Looking at the bike wheel, the most obvious and simplest way of modelling it is as a simple flywheel. This adds a new term to our list of assumptions.

Assumptions

  1. All components are rigid bodies: By assuming this we disregard any bending/torsion/elasticity in our components. Effects like vibrations disappear from our model

  2. The mass of our wheels is evenly distributed: This is not usually the case, as the spokes of a bike wheel have less mass than the main wheel.

Animation#

Note

Please look at the animation page 3D Visualization and Animation for an introduction to how you make animations in Python.

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